LINPACK

A good starting point is LINPACK (Dongarra et al. 1979). The LINPACK project began in the mid-1970s, with the goal of producing a package of mathematical software for solving systems of linear equations. The project developers took a careful look at how one puts together a package of mathematical software and attempted to design a package that would be effective on state-of-the-art computers at that time—the Control Data Corporation (scalar) CDC 7600 and the IBM System 370. Because vector machines were just beginning to emerge, we also provided some vector routines. Specifically, we structured the package around the basic linear algebra subprograms (BLAS) (Lawson et al. 1979) for doing vector operations.

The package incorporated other features, as well. Rather than simply collecting or translating existing algorithms, we reworked algorithms. Instead of the traditional row orientation, we used a column orientation that provided greater efficiency. Further, we published a user's guide with directions and examples for addressing different problems. The result was a carefully designed package of mathematical software, which we released to the public in 1979.